Simplifying Expressions (Collecting Like Terms) - Examples, Exercises and Solutions

Let's simplify the expression $3x + 4x + 7 + 2$ step-by-step:

• Step 1: Combine Like Terms Involving $x$
  The terms $3x$ and $4x$ are like terms because both involve the variable $x$. To combine them, add their coefficients:
  $3x + 4x = (3 + 4)x = 7x$

• Step 2: Combine Constant Terms
  The expression includes constant terms $7$ and $2$. These can be added together to simplify:
  $7 + 2 = 9$

• Step 3: Write the Simplified Expression
  Now, combine the results from Step 1 and Step 2 to form the final simplified expression:
  $7x + 9$

Therefore, the simplified expression is $7x + 9$.

Reviewing the choices provided, the correct choice is:

• Choice 2: $7x + 9$

This matches our simplified expression, confirming our solution is correct.

To solve this problem, we'll follow these steps:

• Step 1: Combine like terms by identifying and adding their coefficients.
• Step 2: Simplify the expression.
• Step 3: Verify the resulting expression with the provided choices.

Let's work through each step:

Step 1: Identify the coefficients in the expression $3z + 19z - 4z$. The coefficients are $3$, $19$, and $-4$.

Step 2: Add and subtract these coefficients: $3 + 19 - 4$.

Step 3: Calculate: $3 + 19 = 22$ and then $22 - 4 = 18$.

Therefore, the simplified expression is $18z$.

The solution to the problem is $18z$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the like terms in the expression.
• Step 2: Combine the constant terms.
• Step 3: Combine the coefficients of $x$.

Now, let's work through each step:
Step 1: The given expression is $11 + 5x - 2x + 8$. There are constants (11 and 8) and terms with $x$ (5x and -2x).
Step 2: Combine the constants: $11 + 8 = 19$.
Step 3: Combine the coefficients of $x$: $5x - 2x = 3x$.

After simplification, the expression becomes $19 + 3x$.

The correct solution from the multiple-choice options is $\boxed{19 + 3x}$.

To simplify the expression $5 + 0 + 8x - 5$, follow these steps:

• Step 1: Identify and group like terms. In this case, there are constants (5, 0, -5) and a term with a variable (8x).
• Step 2: Combine the constants: $5 + 0 - 5$.
• Step 3: Calculate: $5 - 5 = 0$.

Now, our expression simplifies to $0 + 8x$, which is simply $8x$.

Therefore, the simplified expression is $8x$.

To solve this problem, we will simplify the expression $5+8-9+5x-4x$ by separately combining the constants and the variable terms.

Step 1: Simplify the constant terms.
$5 + 8 - 9 = 4$

Step 2: Simplify the variable terms.
$5x - 4x = x$

Step 3: Combine the results from steps 1 and 2.
Thus, the simplified expression is $4 + x$.

Therefore, the solution to the problem is $4 + x$, which corresponds to choice .

To solve this algebraic problem, follow these steps:

• Step 1: Identify the coefficients of the variable $x$ in the expression $x + x$. Here, the coefficient for each $x$ is 1.
• Step 2: Add the coefficients together. This gives $1 + 1 = 2$.
• Step 3: Multiply the result by the variable. This results in $2x$.

Since the problem is a multiple-choice question, review the available choices to select the correct answer. The expression simplifies to $2x$, which corresponds to choice 3: $2x$.

Therefore, the solution to the problem is $2x$.

To determine if the expressions $18x$ and $2 + 9x$ are equivalent, we'll analyze their structures.

• $18x$ is a linear expression with a single term involving the variable $x$, and its coefficient is 18.
• $2 + 9x$ consists of two terms: a constant term $2$ and a linear term $9x$ with coefficient 9.

For two expressions to be equivalent, each corresponding term must be equal. Here, the expression $18x$ has no constant term, whereas $2 + 9x$ has a constant term of 2. Furthermore, the linear term coefficients differ: $18 \neq 9$.

Therefore, the expressions $18x$ and $2 + 9x$ are not the same. They structurally differ and cannot be made equivalent just through similar values of $x$.

Therefore, the solution to this problem is: No.

To solve this problem, we'll analyze the expressions $3+3+3+3$ and $3 \times 4$ to determine if they are equivalent.

First, evaluate the expression $3+3+3+3$:

• Add the numbers: $3 + 3 = 6$
• Add again: $6 + 3 = 9$
• Add the last $3$: $9 + 3 = 12$

The result of $3+3+3+3$ is $12$.

Next, evaluate the expression $3 \times 4$:

• Perform the multiplication: $3 \times 4 = 12$

The result of $3 \times 4$ is also $12$.

Since both expressions result in the same number, we conclude that

The expressions are the same.

Therefore, the correct answer is Yes.

To solve this problem, we'll follow these steps:

• Step 1: Simplify the expression $2 \times 10x$.
• Step 2: Compare the simplified expression with $20x$.

Now, let's work through each step:
Step 1: The expression $2 \times 10x$ can be rewritten using associativity as $2 \times (10 \times x)$.
Step 2: Apply the associative property of multiplication: $(2 \times 10) \times x = 20 \times x = 20x$.

Comparing this with the given expression, we see that both expressions are indeed the same, as they simplify to $20x$.

Therefore, the solution to the problem is Yes.

To simplify the expression $7a + 8b + 4a + 9b$, we will follow these steps:

• Step 1: Identify like terms. The expression contains terms involving $a$ ($7a$ and $4a$) and terms involving $b$ ($8b$ and $9b$).
• Step 2: Combine the coefficients of like terms.
• Step 3: Rewrite the simplified expression.

Step 1: The like terms involving $a$ are $7a$ and $4a$.

Step 2: Add these coefficients: $7 + 4 = 11$. Therefore, the combined term for $a$ is $11a$.

Step 3: The like terms involving $b$ are $8b$ and $9b$.

Step 4: Add these coefficients: $8 + 9 = 17$. Therefore, the combined term for $b$ is $17b$.

Thus, the expression simplifies to $11a + 17b$.

The correct answer choice is: $11a + 17b$.

To solve the exercise, we will reorder the numbers using the substitution property.

$18x-8x+4x-7-9=$

To continue, let's remember an important rule:

1. It is impossible to add or subtract numbers with variables.

That is, we cannot subtract 7 from 8X, for example...

We solve according to the order of arithmetic operations, from left to right:

$18x-8x=10x$$10x+4x=14x$$-7-9=-16$Remember, these two numbers cannot be added or subtracted, so the result is:

$14x-16$

To solve the problem, we should simplify the expression by combining like terms:

• Step 1: Identify like terms.
  • The terms involving $a$ are $13a$ and $-4a$.
  • The terms involving $b$ are $14b$, $-2b$, and $-4b$.
  • The term involving $c$ is $17c$.
• Step 2: Combine like terms by summing their coefficients:
  • For $a$-terms: $13a - 4a = (13 - 4)a = 9a$.
  • For $b$-terms: $14b - 2b - 4b = (14 - 2 - 4)b = 8b$.
  The $c$ term remains unchanged as $17c$.

Therefore, the simplified expression is $9a + 8b + 17c$.

Checking the choices provided, we see that the correct answer is $9a + 8b + 17c$, which matches choice .

Thus, the final simplified expression is $9a + 8b + 17c$.

To solve this problem, we'll follow these steps:

• Step 1: Identify and group like terms.
• Step 2: Combine the coefficients for each type of term.

Let's begin the simplification process:

First, we identify and group the like terms in the expression $a + b + bc + 9a + 10b + 3c$.

Notice: - The terms involving $a$ are $a$ and $9a$. - The terms involving $b$ are $b$ and $10b$. - The terms involving $c$ are $3c$, and the multiplication term with $c$ is $bc$.

Step 2: Combine the like terms:

$a + 9a = 10a$

$b + 10b = 11b$

The term $bc$ can be rearranged with $3c$ as $(b+3)c$.

Thus, after combining the terms, we have:

$10a + 11b + (b + 3)c$.

Therefore, the simplified form of the expression is:

$10a + 11b + (b + 3)c$

To solve this problem, we'll follow these steps:

• Identify and group like terms within the expression.
• Combine the coefficients of these like terms.
• Simplify the expression by adding or subtracting coefficients.

Now, let's work through each step:

Step 1: Observe the given algebraic expression:
    $35m + 9n - 48m + 52n$.

Step 2: Group like terms, separating terms with $m$ from those with $n$:
    $(35m - 48m)$ and $(9n + 52n)$.

Step 3: Combine the terms with $m$:
    $35m - 48m = (35 - 48)m = -13m$.

Step 4: Combine the terms with $n$:
    $9n + 52n = (9 + 52)n = 61n$.

Therefore, the simplified form of the expression is:
    $61n - 13m$.

This leads to our final solution:

$61n - 13m$

In order to solve this question, remember that we can perform the addition and subtraction operations when we have the same variable.
However we are limited when we have several different variables.
 

Note that in this exercise that we have three variables:
$45$ which has no variable
$8y$ and $34y$ which both have the variable $y$
and $45z$ with the variable $z$

Therefore, we can only operate with the y variable, since it's the only one that exists in more than one term.

Rearrange the exercise:

$45-34y+8y-45z$

Combine the relevant terms with $y$

$45-26y-45z$

We observe that this is similar to one of the other answers, with a small rearrangement of the terms:

$-26y+45-45z$

Given that we have no possibility to perform additional operations - this is the solution!